This may seem a strange question but if I connected a CB radio to the standard antenna that comes with my car for its stereo would it work if I fitted a filter/splitter to it to attach both the CB and the stereo?

No this wouldn't work and would probably damage the output transistors in your CB radio. It is because the stereo antenna would not be tuned anywhere near the CB frequency of 27MHz and the SWR would be off the scale...